In an embodiment, a processor includes at least one core including a first core. The first core includes memory execution logic to execute one or more memory instructions, memory dispatch logic to output a plurality of memory instructions to the memory execution logic, and reactive memory instruction tracking logic. The reactive memory instruction tracking logic is to detect an onset of a memory instruction high power event associated with execution of at least one of the memory instructions, and to indicate to the memory dispatch logic to throttle output of the memory instructions to the memory execution logic responsive to detection of the onset of the memory instruction high power event. The processor also includes cache memory coupled to the at least one core. Other embodiments are described and claimed.